Moses Swaibu's 49th-minute own goal and Chung-Yong Lee's clinical finish less than 60 seconds later put Wanderers on course to victory against a team 72 positions below them in the Football League ladder.
Gary Cahill and substitute Mark Davies added two late goals to help Bolton reach the fourth round of the FA Cup for the first time in three years.
First-team coach Steve Wigley and assistant manager Chris Evans took charge of Wanderers following Gary Megson's sacking on Wednesday.
But if the home supporters were hoping for a brand new dawn then they were sadly mistaken in an uninspiring first half at the Reebok with little to choose between the two sides.
Cahill came closest to breaking the deadlock in the first period when he meet Matt Taylor's corner but his header was hooked off the line by Matthew Saunders on 27 minutes.
But Wanderers burst into life at the start of the second half. First Taylor's superb cross struck Swaibu and went in.
And less than 60 seconds later, the game was effectively over when Ivan Klasnic picked out Lee and the South Korean slotted home with aplomb.
Taylor nearly made it three when he rattled the crossbar following a mad scramble in the Imps' penalty area.
Lincoln refused to give up and Chris Herd would have pulled one back for the plucky visitors but for a wonderful save from Ali Al-Habsi to tip over his deflected strike on 71 minutes.
But it was Wanderers who had the final say. Kevin Davies picked out Cahill and he planted a firm header past Rob Burch on 83 minutes before Mark Davies turned in Paul Robinson's cross in injury time to give the scoreline a flattering look.